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arXiv · 1908.05420

A toy model for the Drinfeld-Lafforgue shtuka construction

D. Gaitsgory·D. Kazhdan·N. Rozenblyum·Y. Varshavsky
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Abstract

The goal of this paper is to provide a categorical framework that leads to the definition of shtukas \`a la Drinfeld and of excursion operators \`a la V. Lafforgue. We take as the point of departure the Hecke action of Rep(G^L) on the category Shv(Bun_G) of sheaves on Bun_G, and also the endofunctor of the latter category, given by the action of the geometric Frobenius. The shtuka construction will be obtained by applying (various versions of) categorical trace.

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D. Gaitsgory, D. Kazhdan, N. Rozenblyum, Y. Varshavsky. 2019-08-15. A toy model for the Drinfeld-Lafforgue shtuka construction. https://arxiv.org/abs/1908.05420

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